Find the quotient:
- (i) 23 ÷ 310
- (ii) 711 ÷ 58
- (iii) −47 ÷ 514
Answer: (i) 209 (ii) 5655 (iii) −85
Step-by-step solution
Idea: ab ÷ cd = ab × dc: keep the first number, turn the second upside down (its reciprocal) and multiply.
(i) 23 ÷ 310
- 23 × 103.½ mark
- = 209 (= 229).½ mark
209
(ii) 711 ÷ 58
- 711 × 85.½ mark
- = 5655.½ mark
5655
(iii) −47 ÷ 514
- −47 × 145 = −5635.½ mark
- Divide top and bottom by 7: −85.½ mark
−85
(i) 20/9 (ii) 56/55 (iii) −8/5
Check: Multiply back: 209 × 310 = 6090 = 23 ✓; 5655 × 58 = 280440 = 711 ✓; −85 × 514 = −4070 = −47 ✓.
Answer to write in the exam
(i)
23 ÷ 310 = 23 × 103
= 209
(ii)
711 ÷ 58 = 711 × 85
= 5655
(iii)
−47 ÷ 514 = −47 × 145 = −5635
= −85
Common mistakes that cost marks
- Turning the first fraction upside down instead of the second.
- Dividing numerators and denominators directly: 23 ÷ 310 = 2÷33÷10 — messy and easy to get wrong; multiply by the reciprocal.
- In (iii), giving +85. Negative ÷ positive is negative.
How this can come in the exam
MCQ (1 mark)
The reciprocal of −37 is
- 37
- 73
- −73
- −37
Show answer
(C) −73
−37 × −73 = 1, so the reciprocal is −73 (the sign stays).
Short answer (2 marks)
How many pieces of length 38 m can be cut from a ribbon of length 154 m?
Show answer
154 ÷ 38 = 154 × 83 (1 mark) = 12012 = 10 pieces (1 mark).Try one yourself
Find −1225 ÷ −815.
Show answer
−1225 × 15−8 = 180200 = 910.
More questions like this
- Show that: (12 + 34) × 83 = 12 × 83 + 34 × 83.
- Simplify the following using the distributive property: 79(67 − 34).
- Find the rational number x such that: 56(x + 35) = 56x + 12.
- Try and represent 85 and −74 on a number line.
- The absolute value of a rational number x, written as |x|, represents its distance from 0 on the number line. |53| = 53, |−53| is also equal to 53 and |0| = 0.